Quantum Cosmological Relational Model of Shape and Scale in 1-d

TL;DR

This paper extends 1-d relational particle models to include scale, creating a closer analogy with quantum cosmology and enabling quantum-level studies of the problem of time and structure formation.

Contribution

It introduces scale into 1-d relational particle models, strengthening their analogy with quantum cosmology and allowing tractable quantum models with cosmological features.

Findings

Models include analogues of spatial curvature, cosmological constant, dust, and radiation.

Several models are solvable at the quantum level.

Supports studies of the problem of time and structure formation in quantum cosmology.

Abstract

Relational particle models are useful toy models for quantum cosmology and the problem of time in quantum general relativity. This paper shows how to extend existing work on concrete examples of relational particle models in 1-d to include a notion of scale. This is useful as regards forming a tight analogy with quantum cosmology and the emergent semiclassical time and hidden time approaches to the problem of time. This paper shows furthermore that the correspondence between relational particle models and classical and quantum cosmology can be strengthened using judicious choices of the mechanical potential. This gives relational particle mechanics models with analogues of spatial curvature, cosmological constant, dust and radiation terms. A number of these models are then tractable at the quantum level. These models can be used to study important issues 1) in canonical quantum gravity: the problem of time, the semiclassical approach to it and timeless approaches to it (such as the naive Schrodinger interpretation and records theory). 2) In quantum cosmology, such as in the investigation of uniform states, robustness, and the qualitative understanding of the origin of structure formation.